Excluding subdivisions of infinite cliques

Robertson, Neil; Seymour, P. D.; Thomas, Robin

doi:10.1090/S0002-9947-1992-1079057-3

Excluding subdivisions of infinite cliques
HTML articles powered by AMS MathViewer

by Neil Robertson, P. D. Seymour and Robin Thomas PDF

Trans. Amer. Math. Soc. 332 (1992), 211-223 Request permission

Abstract:

For every infinite cardinal $k$ we characterize graphs not containing a subdivision of ${K_k}$.

References

Dan Bienstock, Neil Robertson, Paul Seymour, and Robin Thomas, Quickly excluding a forest, J. Combin. Theory Ser. B 52 (1991), no. 2, 274–283. MR 1110475, DOI 10.1016/0095-8956(91)90068-U
Reinhard Diestel, Graph decompositions, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1990. A study in infinite graph theory. MR 1078627
R. Halin, Unterteilungen vollständiger Graphen in Graphen mit unendlicher chromatischer Zahl, Abh. Math. Sem. Univ. Hamburg 31 (1967), 156–165 (German). MR 229548, DOI 10.1007/BF02992395
Igor Kříž and Robin Thomas, Clique-sums, tree-decompositions and compactness, Discrete Math. 81 (1990), no. 2, 177–185. MR 1054976, DOI 10.1016/0012-365X(90)90150-G
Neil Robertson and P. D. Seymour, Graph minors. I. Excluding a forest, J. Combin. Theory Ser. B 35 (1983), no. 1, 39–61. MR 723569, DOI 10.1016/0095-8956(83)90079-5
Neil Robertson and P. D. Seymour, Graph minors. III. Planar tree-width, J. Combin. Theory Ser. B 36 (1984), no. 1, 49–64. MR 742386, DOI 10.1016/0095-8956(84)90013-3
Neil Robertson, Paul Seymour, and Robin Thomas, Excluding infinite minors, Discrete Math. 95 (1991), no. 1-3, 303–319. Directions in infinite graph theory and combinatorics (Cambridge, 1989). MR 1141945, DOI 10.1016/0012-365X(91)90343-Z
P. D. Seymour and Robin Thomas, Excluding infinite trees, Trans. Amer. Math. Soc. 335 (1993), no. 2, 597–630. MR 1079058, DOI 10.1090/S0002-9947-1993-1079058-6
Paul Seymour and Robin Thomas, An end-faithful spanning tree counterexample, Proc. Amer. Math. Soc. 113 (1991), no. 4, 1163–1171. MR 1045600, DOI 10.1090/S0002-9939-1991-1045600-8